A quartermaster was a person assigned to supplying people of an organization.
During the 22nd century, Earth starships like Enterprise NX-01 had their own quartermasters, who oversaw the ship's supplies. (ENT: "Civilization", "Fortunate Son")
Enterprise's quartermaster is referred to in the final edit of "Fortunate Son", the episode's first draft script omitted that reference, instead referring to the ship's stores.
The Starfleet Quartermaster was responsible for Starfleet supplies like ration packs. (ENT: "Countdown")
The USS Enterprise had a quartermaster, also responsible for providing attire to crew members and guests. James T. Kirk said to Spock (referring to Captain Christopher), "Why don't you have the quartermaster issue him something more suitable?" (TOS: "Tomorrow is Yesterday")
In 2269, Spock requested a Vulcan desert soft-suit and boots, a small selection of street wear and carry bag, circa 8877 Vulcan years, for an expedition back in time. These supplies were issued by the quartermaster's wardrobe section. (TAS: "Yesteryear")
Klim Dokachin was the Zakdorn quartermaster of Surplus Depot Z15 in 2368. (TNG: "Unification I")
Starfleet Chief Edgar Willoughby was the quartermaster for the Bajoran sector in 2375. (DS9: "Treachery, Faith and the Great River")